The paper presents an empirical analysis of a model of endogenous growth and innovation with unequal incomes and hierarchical consumer demand. The theoretical model predicts a positive impact of income inequality on product diversity. The impact of inequality on per-capita growth may be positive or negative depending upon the assumptions about productivity growth, where the standard assumption that productivity is positively related to product diversity implies a positive impact. In the empirical part, indices for absolute and relative product diversity are calculated from ICP-expenditure data. The empirical evidence shows that a significant positive relationship exists between income inequality and relative product diversity and that the relationship between income inequality and economic growth is negative and significant. The results lead to the conclusion that the diversity-productivity relationship used in new growth theory has to be treated with scepticism.